KaliyanaB396319 KaliyanaB396319
  • 25-10-2022
  • Mathematics
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Solve the following equations. (You may leave your answer in terms of logarithms or you can plug your answer into a calculator to get a decimal approximation.)

Solve the following equations You may leave your answer in terms of logarithms or you can plug your answer into a calculator to get a decimal approximation class=

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ToprakR725417 ToprakR725417
  • 25-10-2022

Given the equation:

[tex]200(1.06)^t=550[/tex]

We divide each side by 200:

[tex]\begin{gathered} \frac{200}{200}(1.06)^t=\frac{550}{200} \\ 1.06^t=2.75 \end{gathered}[/tex]

Now, we take the natural logarithm:

[tex]\begin{gathered} \ln (1.06^t)=\ln (2.75) \\ t\cdot\ln (1.06)=\ln (2.75) \\ \therefore t=\frac{\ln (2.75)}{\ln (1.06)} \end{gathered}[/tex]

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